Determine Maximum Magnitude P for Shear Stress of Beam

In summary, the problem involves determining the maximum load, P, that a beam supported by a pin at A and a short link BC can withstand without exceeding an average shear stress of 80 MPa. The pins have a diameter of 18 mm. After finding the required shear force in the pins, an error is made by assuming a support reaction B_y at joint B, when in fact there is no external support there. The method is otherwise correct and the solution for P can be obtained after eliminating the extra term. It is also important to check that the pin at A does not control the design.
  • #1
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Homework Statement

Question 3: The beam is supported by a pin at A and a short link BC, as shown in Figure 3.0. Determine the maximum magnitude P of the loads the beam will support if the average shear stress in each pin is not to exceed 80 MPa. The diameter for each of the pins is 18 mm.

http://img13.imageshack.us/img13/7517/chibusq3.jpg [Broken]

Homework Equations


The Attempt at a Solution



http://img5.imageshack.us/img5/1824/chibus1.jpg [Broken]
http://img13.imageshack.us/img13/9589/chibus2.jpg [Broken]

I just wanted to get an idea if I'm way off. Really I don't know how to proceed past finding the required shear force in the pins to shear them.

PS: Sorry for my horrible english and writing skills.
 
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  • #2
Hello, Chibus, welcome to PF! You are making an error in assuming that there is a support reaction B_y at joint B. There is no external support there. B_y is just the vertical component of the force in the link. Don't add it in twice. Otherwise, your method looks OK, and you should be able to solve for P when you eliminate that extra term. Also, be sure to check that the pin at A does not control the design.
 
  • #3


Dear student,

Thank you for your question. Based on your attempt at a solution, it seems that you are on the right track. To determine the maximum magnitude P for shear stress of the beam, we need to consider the maximum shear stress that each pin can withstand and ensure that the average shear stress in each pin does not exceed 80 MPa.

To do this, we can use the formula for shear stress in a circular cross-section, which is:

τ = (4/π) * (F/A)

Where τ is the shear stress, F is the applied force, and A is the cross-sectional area.

In this case, we can calculate the cross-sectional area of each pin using the given diameter of 18 mm. Once we have the cross-sectional area, we can then determine the maximum force that each pin can withstand without exceeding 80 MPa. This will give us the maximum magnitude P for the shear stress of the beam.

I hope this helps. If you have any further questions, please feel free to ask. Keep up the good work!

Best regards,
 

1. What is the maximum magnitude of shear stress for a beam?

The maximum magnitude of shear stress for a beam is the highest amount of stress that the beam can withstand before it fails. It is a critical factor in the design and analysis of beams, as exceeding this maximum limit can lead to structural failure.

2. How is the maximum magnitude of shear stress determined for a beam?

The maximum magnitude of shear stress for a beam is determined by calculating the shear force and dividing it by the cross-sectional area of the beam. This value is then compared to the shear stress limit of the material to determine the maximum magnitude of shear stress.

3. What factors can affect the maximum magnitude of shear stress for a beam?

The maximum magnitude of shear stress for a beam can be affected by several factors, including the material properties of the beam, the shape and size of the beam, the type and magnitude of the applied load, and the support conditions of the beam.

4. Why is it important to determine the maximum magnitude of shear stress for a beam?

Determining the maximum magnitude of shear stress for a beam is crucial in ensuring the structural integrity and safety of the beam. It helps engineers and designers select the appropriate materials, dimensions, and support for the beam to withstand the expected loads and prevent failure.

5. How can the maximum magnitude of shear stress be increased in a beam?

The maximum magnitude of shear stress in a beam can be increased by increasing the cross-sectional area of the beam, using stronger materials, changing the beam's shape or support conditions, or redistributing the load to other parts of the beam.

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